How do i know if rendering my animation is finished,
There are three things you can look for.

Most of the information that will be useful to you is in the Render Result view of the Image Editor window. The Render Result usually comes up automatically when you start rendering. You can also bring it up by pressing F11.

This is by far the best place to get information about a render process.

At the top of this window is a row of text that has information about the render. As a frame is rendering, it will show the number of the last tile that finished, or the number of samples done/remaining. It will also show information "between" frames about loading images, synchronizing geometry, calculating BVH caches, and stuff like that. That should give you some indication of whether the render is busy with something or not.

In the image below, you can see the bar I'm talking about says:


  "Mem: 17.09M Peak:17.09M | Time: xxxxxx | Done | path Tracing Sample 10/10"


That text will be a little different depending on a number of factors (like image vs. animation), but that's what you're looking for.





Another thing you can look at is the render progress bar. It will show the progress for each frame (not the whole animation), but if the progress bar isn't being displayed at all, then Blender isn't rendering.



Blender provides pretty good feedback while rendering, so the previous two solutions should be plenty. If, however, you want to look at something else, the last thing you can check is the output file. You should be rendering the frames as individual images (for a host of reasons). You should be able to look at the creation time of each image and determine how long to wait for the next one. If the next one takes too long, you can use that to determine if it's still rendering.

If you're rendering to a video file, you can still look at the size of that file, and it should be increasing regularly as each frame is finished.